"The food is ours."
to denote ownership you can use two constructs:
quelque chose + conjugation of être + à + stressed pronoun (moi, lui, nous, etc.)
quelque chose + conjugation of être + possessive pronoun (le mien, le sein, le notre, etc.)
However they are not interchangeable. And worse the lack of interchangeability appears illogical since although la nourriture est la notre is incorrect it seems odd that cette nourriture est la notre is correct even though they appear to exhibit the same type of structure, namely:
noun + conjugation of être + possessive pronoun
The reason is because when you are saying something belongs to someone, it is important to consider whether there is a choice when identifying the something. This concept is best explained as follows:
ce sandwich est le sien implies there is a choice between several sandwiches (for example a plate of sandwiches).
ce sandwich est à lui implies there is either a choice or there is just a lonesome sandwich
Following this logic la nourriture est à nous is correct whereas if you tried to use la nourriture est la notre you would be saying:
The food (amongst many foods) belongs to us. But in this context the sentence wouldn’t distinguish our food from the other foods. To distinguish our food from the other foods you would need to use a demonstrative adjective.
A demonstrative adjective (ce, cet, cette, ces) + noun + possessive pronoun is commonly used when there is choice concerning the ownership of something
Also you could say:
la nourriture, c’est la Notre because c’est with a possessive pronoun is commonly used
c’est le mien / il est à moi - it is mine.
J’ai trouvé ce livre. Est-ce le vôtre ? - I found this book. Is it yours ?